Anyone who drinks several cups of coffee daily and quits cold turkey can get headaches. Starbucks brand has a great tasting single-cup instant -- I get it in the grocery. First time I tasted it was about 5 AM one morning on top of Mt Whitney. A JMT finisher found me sleeping in the hut, and offered me a cup. It was great! (I now keep it around the house.)
You guys need to try Diamox. I, myself, would not go to Horseshoe Meadows without it, let alone hike out of there! (The PA in your group should read up on it.)
A person vomiting is on the verge of serious trouble. It appears you were ok staying, since the he/she improved. However, it could have gone the other way. Leaving someone alone after that could lead to serious trouble. If someone could check up on them each hour, and if the situation worsens, get them the h**l out of there!!!
Two things seem to make AMS worse: Exertion (that 40 lb pack weight), and ALSO hydration. You did not mention it... Was everyone consciously drinking enough? When the appetite goes, so can thirst. I always make sure I drink more than enough to satisfy my thirst when I am at altitude. Peeing clear is the indicator that you're ok. Using a pee-bottle at night makes it easier for me -- otherwise I would limit my liquid intake before bed, which is not good for the AMS.